Multivalent Diffusive Transport

Abstract

We present here a model for multivalent diffusive transport whereby a central point-like hub is coupled to multiple feet, which bind to complementary sites on a two-dimensional landscape. The available number of binding interactions is dependent on the number of feet (multivalency) and on their allowed distance from the central hub (span). Using Monte Carlo simulations that implement the Gillespie algorithm, we simulate multivalent diffusive transport processes for 100 distinct walker designs. Informed by our simulation results, we derive an analytical expression for the diffusion coefficient of a general multivalent diffusive process as a function of multivalency, span, and dissociation constant K d. Our findings can be used to guide the experimental design of multivalent transporters, in particular, providing insight into how to overcome trade-offs between diffusivity and processivity.

The nanocaterpillar's random walk: diffusion with ligand–receptor contacts

“…This slow down is due to spring recoil forces acting over longer times, eventually freezing the particle in a given location. Note that similar qualitative dependencies of the diffusion coefficient on the unbinding rate ( D eff ∼ k B Tq off / k ) were noted in a numerical model of multivalent transport on discrete sites, 44 in a scaling law investigation of sticky reptation in polymers, 62 and experimentally in Influenza A viruses. 19…”

“…22,40 To make progress, numerical and analytical models often rely on simplified assumptions, e.g. excluding stochastic relaxation of the legs, 41,42 limiting the analysis to a small number of legs, 41,43,44 or assuming small perturbations. 22 Such models have given insight into a variety of phenomena, such as how specific parameters could favor rolling over sliding 7,41,43,45,46 or how specific mechanisms could increase overall mobility (with coupling effects such as binding dynamics depending on bond number [47][48][49] or when numerous adhesive sites are available for a single ligand 22,50,51 ).…”

An Artificial Protein-Based Burnt-Bridges Molecular Motor Design

“…This latter model demonstrated the importance of balancing chemical kinetic rates of multiple interacting tethers with the timescale of bead diffusion. Interestingly, saltatory dynamics have not been observed in monowheel-like designs implementing nanoscale hubs [38,46], demonstrating the role that polyvalency can have in influencing motility [47][48][49]. The lawnmower: an artificial protein-based burnt-bridge molecular motor LMs can occupy at least two distinct dynamical states, similar to previous synthetic microsphere-based systems.…”

“…This latter model demonstrated the importance of balancing chemical kinetic rates of multiple interacting tethers with the timescale of bead diffusion. Interestingly, saltatory dynamics have not been observed in monowheel-like designs implementing nanoscale hubs [38,46], demonstrating the role that polyvalency can have in influencing motility [47][48][49].…”

Through the Eyes of Creators: Observing Artificial Molecular Motors

“…The performance characteristics of synthetic BBR systems often vary with their polyvalency, that is, with the number of available molecular chemical units (“feet”) capable of binding to, and cleaving, substrate sites. ,− Currently, various synthetic BBRs have been realized, both at the nanoscale ,,,,− and microscale. ,, …”